Shuttlecock

Abstract

The badminton racket 2 has a racket shaft 4, a racket handle 10 for insertion of the racket shaft 4 near a rear end 20 thereof, and a racket frame 6 mounted near a front end 22 of the racket shaft 4. The out-of-plane first natural frequency ωol (Hz) and the out-of-plane second natural frequency ωo2 (Hz) in the natural vibration of the badminton racket 2 under a free constraint condition satisfy the following mathematical expression: ωo2 ≥ 2.5 x ωol + 37.0.

Description

Technical Field

[0001] This instruction manual discloses a racket for badminton. Background Technology

[0002] A badminton racket has a frame, strings, and a shaft. The frame has a top and a bottom. The strings form the string face. A player hits the shuttlecock with the racket. Upon impact, the string face collides with the shuttlecock. The impact from the collision is transmitted from the strings through the frame to the shaft. Upon impact, the frame and shaft deform. Attempts to optimize the deformation behavior upon impact are documented in JP Patent Application Publication 2001-70481.

[0003] Existing technical documents

[0004] Patent documents

[0005] Patent Document 1: JP 2001-70481 Summary of the Invention

[0006] The problem that the invention aims to solve

[0007] In badminton, players use a variety of shots, including smashes, lobbing, drops, and clears.

[0008] A lob is a common shot hit by a player from near the net on the court. A lob is a shot intended to send the shuttlecock behind the opponent's court. The shuttlecock's trajectory is high in a lob. The skill of sending the shuttlecock at a predetermined height is essential for players. Players who frequently use lobs desire a consistent shuttlecock trajectory (speed, height, etc.).

[0009] In a statistically based survey, the typical contact point for a lob shot is near the top of the frame. However, in other shots besides the lob, the shuttlecock can also be hit from a point near the top of the frame.

[0010] A cut lobbing differs from a regular lob shot in that it involves a slicing motion. In a cut lobbing, the shuttlecock spins and flies at high speed. Cut lobbing is commonly seen when players hit the shuttlecock near the net on the court. The aim of a cut lobbing is to send the shuttlecock to the back of the opponent's court. The shuttlecock's trajectory is high in a cut lobbing. The skill to send the shuttlecock at a predetermined height is essential for players. Players who frequently use cut lobbing aim for consistency in the shuttlecock's trajectory (speed, height, etc.).

[0011] In a statistically based survey, the typical hitting point for a slice shot is near the top of the frame. However, for other shots besides the slice shot, the shuttlecock can also be hit from a point near the top of the frame.

[0012] The applicant's objective is to provide a badminton racket that can suppress ballistic deviation of the shuttlecock during a shot with the hitting point close to the top of the frame.

[0013] Methods for solving problems

[0014] The preferred badminton racket has the following features:

[0015] A racket handle with a butt end and a tip end;

[0016] A grip for inserting near the rear end of the racket shaft; and

[0017] The racket frame is mounted on the shaft near the front end. The out-of-plane first natural frequency ωo1 (Hz) and out-of-plane second natural frequency ωo2 (Hz) in the natural vibration under free constraint conditions satisfy the following mathematical formula (I-1).

[0018] ωo2≥2.5×ωo1+37.0(I-1)

[0019] The effects of the invention

[0020] Players using this badminton racket can easily hit the shuttlecock with the contact point closer to the top of the frame. This racket can contribute to victory in matches. Attached Figure Description

[0021] [ Figure 1 ] Figure 1 This is a front view of a badminton racket according to one embodiment.

[0022] [ Figure 2 ] Figure 2 It means Figure 1 The right-side view of the racket.

[0023] [ Figure 3 ] Figure 3 It means Figure 1 An enlarged cross-sectional view of a portion of the racket shaft.

[0024] [ Figure 4 ] Figure 4 It is along Figure 3 Enlarged cross-sectional view of line IV-IV.

[0025] [ Figure 5 ] Figure 5 It means Figure 1 The unfolded diagram of the prepreg sheet used for the racket shaft.

[0026] [ Figure 6 ] Figure 6 It means Figure 1 A diagram illustrating the method for determining the out-of-plane natural frequency of a racket.

[0027] [ Figure 7 ] Figure 7 It means through Figure 6 The results of the measurement are shown in the figure.

[0028] [ Figure 8 ] Figure 8 It means Figure 1 A graph showing the relationship between the out-of-plane first-order natural frequency ωo1 and the out-of-plane second-order natural frequency ωo2 of a badminton racket.

[0029] [ Figure 9 ] Figure 9 A development diagram showing a prepreg sheet for the shaft of a badminton racket according to other embodiments.

[0030] [ Figure 10 ] Figure 10 This is an explanatory diagram illustrating the method for measuring the in-plane natural vibration frequency of a racket.

[0031] [ Figure 11 ] Figure 11 It means through Figure 10 The results of the measurement are shown in the figure.

[0032] [ Figure 12 ] Figure 12 It means through Figure 10 The graph shows the relationship between the in-plane first-order natural frequency ωi1 and the in-plane second-order natural frequency ωi2 obtained by measurement.

[0033] [ Figure 13 ] Figure 13 This is a development diagram showing the prepreg sheet for the shaft of the badminton racket of Example I-10.

[0034] [ Figure 14 ] Figure 14 This is a development diagram showing the prepreg sheet for the shaft of the badminton racket according to Embodiment I-7.

[0035] [ Figure 15 ] Figure 15 This is a development diagram showing the prepreg sheet for the shaft of the badminton racket of Example II-7.

[0036] Symbol Explanation

[0037] 2…badminton racket

[0038] 4… racket shaft

[0039] 6… Racquet frame

[0040] 8…pat the neck

[0041] 10…handle

[0042] 12…string beats

[0043] 14…Rear

[0044] 16…Central region

[0045] 18…Front

[0046] 20…backend

[0047] 22…Frontend

[0048] 24…Top of frame

[0049] 26…Bottom of the frame

[0050] 28… (transverse thread)

[0051] 30… (vertical line)

[0052] 32…beat the string surface

[0053] 34…Exposed area

[0054] 38…Acceleration pick-up

[0055] S1…First Sheet

[0056] S2…Second sheet

[0057] S3…Third sheet

[0058] S4…Fourth sheet material

[0059] S5…Fifth Sheet

[0060] S6…Sixth Sheet

[0061] S7…Seventh Sheet

[0062] S8…Eighth Sheet

[0063] S9… Ninth Sheet Detailed Implementation

[0064] Hereinafter, preferred embodiments will be described in detail with reference to the accompanying drawings.

[0065] Figure 1 and Figure 2 This refers to badminton racket 2. This racket 2 has a shaft 4, frame 6, neck 8, cap 9, handle 10, and strings 12. Figure 1 and Figure 2 In the diagram, arrow X represents the width direction, arrow Y represents the axial direction, and arrow Z represents the thickness direction.

[0066] The shaft 4 has a rear portion 14, a middle portion 16, and a front portion 18. The shaft 4 further has a rear end 20 and a front end 22. The shaft 4 is hollow. The shaft 4 is formed of fiber-reinforced resin. This fiber-reinforced resin has a resin matrix and multiple reinforcing fibers. The shaft 4 comprises multiple fiber-reinforced layers (described in detail later).

[0067] Examples of thermosetting resins used as the base material for the shaft 4 include epoxy resins, bismaleimide resins, polyimide, and phenolic resins; and thermoplastic resins such as polyetheretherketone, polyethersulfone, polyetherimide, polyphenylene sulfide, polyamide, and polypropylene. Epoxy resin is particularly suitable for the shaft 4.

[0068] Examples of reinforcing fibers for the shaft 4 include carbon fiber, metal fiber, glass fiber, and aramid fiber. Carbon fiber is particularly suitable for the shaft 4. Various fibers can be used in combination.

[0069] The frame 6 is ring-shaped and hollow. The frame 6 is formed of fiber-reinforced resin. This fiber-reinforced resin can be the same as the base resin of the shaft 4. This fiber-reinforced resin can also use the same reinforcing fibers as the reinforcing fibers of the shaft 4. The frame 6 is securely bonded to the front end 22 of the shaft 4 via the neck 8. The frame 6 has a top 24 and a bottom 26.

[0070] The handle 10 has a hole 27 extending in the axial direction (Y direction). The rear end 20 of the shaft 4 is inserted into this hole 27. The inner circumferential surface of the hole 27 and the outer circumferential surface of the shaft 4 are joined with adhesive.

[0071] The string 12 is attached to the frame 6. The string 12 is attached along the width direction X and the axis Y. The portion of the string 12 extending along the width direction X is called the transverse line 28. The portion of the string 12 extending along the axis Y is called the longitudinal line 30. A string surface 32 is formed by multiple transverse lines 28 and multiple longitudinal lines 30. The string surface 32 is approximately along the XY plane.

[0072] exist Figure 1 In the diagram, symbol 34 indicates the exposed portion of the shaft 4. The exposed portion 34 protrudes from the neck 8 and also from the handle 10. Figure 1 In this text, the symbol L represents the length of the exposed portion 34. The length L is typically between 150mm and 210mm.

[0073] Figure 3 It means Figure 1 An enlarged cross-sectional view of a portion of the shaft 4 of racket 2. Figure 4 It is along Figure 3An enlarged cross-sectional view of line IV-IV. As mentioned above, the shaft 4 is hollow. Figure 4 As shown, the cross-sectional shape of the racket shaft 4 is circular. In other words, the racket shaft 4 is cylindrical.

[0074] exist Figure 3 and Figure 4 In the diagram, arrow Di indicates the inner diameter of the shaft 4. A typical inner diameter Di is 3mm or more but less than 10mm. Figure 3 and Figure 4 In the diagram, arrow Do indicates the outer diameter of the shaft 4. A typical outer diameter Do is 5mm or more but less than 15mm.

[0075] As described above, the shaft 4 is formed of fiber-reinforced resin. The shaft 4 can be manufactured using a sheet winding method. In this sheet winding method, multiple prepreg sheets are wound onto a mandrel. Each prepreg sheet has multiple fibers and a matrix resin. The matrix resin is uncured.

[0076] Figure 5 It means Figure 1 The racket 2 has a prepreg sheet structure for its shaft 4. This prepreg sheet structure has nine prepreg sheets (i.e., sheets). Specifically, the prepreg sheet structure has a first sheet S1, a second sheet S2, a third sheet S3, a fourth sheet S4, a fifth sheet S5, a sixth sheet S6, a seventh sheet S7, an eighth sheet S8, and a ninth sheet S9. Multiple fiber reinforcement layers are formed from these prepreg sheets using a method described later. Specifically, the first fiber reinforcement layer is formed from the first sheet S1, the second fiber reinforcement layer from the second sheet S2, the third fiber reinforcement layer from the third sheet S3, the fourth fiber reinforcement layer from the fourth sheet S4, the fifth fiber reinforcement layer from the fifth sheet S5, the sixth fiber reinforcement layer from the sixth sheet S6, the seventh fiber reinforcement layer from the seventh sheet S7, the eighth fiber reinforcement layer from the eighth sheet S8, and the ninth fiber reinforcement layer from the ninth sheet S9.

[0077] Figure 5 The left and right directions in the middle are the axial directions of the racket shaft 4. Figure 5 In the diagram, the positions of backend 20 and frontend 22 are indicated by arrows. For ease of explanation, in... Figure 5 In this case, the scale is inaccurate.

[0078] A first sheet S1 is distributed throughout the entire shaft 4. The first sheet S1 is approximately rectangular in shape. The first sheet S1 comprises a plurality of carbon fibers arranged side by side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is 30° or more and 60° or less. In this embodiment, the angle is 45°. The first sheet S1 has a width of 102 mm and a length of 340 mm.

[0079] The second sheet S2 is distributed throughout the entire shaft 4. The second sheet S2 is approximately rectangular in shape. It comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is -60° or more and -30° or less. In this embodiment, the angle is -45°. The second sheet S2 has a width of 102 mm and a length of 340 mm.

[0080] The carbon fibers in the second sheet S2 are tilted in the opposite direction to those in the first sheet S1. Therefore, the carbon fibers in the second fiber reinforcement layer are tilted in the opposite direction to those in the first fiber reinforcement layer. In this racket shaft 4, a bias structure is achieved through the first and second fiber reinforcement layers. The first and second fiber reinforcement layers contribute to the bending and torsional stiffness of the racket shaft 4. The first and second fiber reinforcement layers are particularly beneficial to the torsional stiffness of the racket shaft 4.

[0081] The third sheet S3 is biasedly located on the front end 22 side of the shaft 4. The third sheet S3 is approximately trapezoidal in shape. This third sheet S3 comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is 30° or more and 60° or less. In this embodiment, this angle is 45°. The third sheet S3 has a width of 36 mm, a length of 185 mm for the upper base, and a length of 195 mm for the lower base.

[0082] The fourth sheet S4 is biasedly located on the front end 22 side of the shaft 4. Axially, the position of the fourth sheet S4 coincides with that of the third sheet S3. The fourth sheet S4 is approximately trapezoidal in shape. This fourth sheet S4 comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is -60° or more and -30° or less. In this embodiment, this angle is -45°. The fourth sheet S4 has a width of 36 mm, a length of 185 mm for the upper base, and a length of 195 mm for the lower base.

[0083] The carbon fibers in the fourth sheet S4 are tilted in the opposite direction to those in the third sheet S3. Therefore, the carbon fibers in the fourth fiber reinforcement layer are tilted in the opposite direction to those in the third fiber reinforcement layer. In this shaft 4, an offset structure is achieved through the third and fourth fiber reinforcement layers. The third and fourth fiber reinforcement layers contribute to the bending stiffness and torsional stiffness of the middle section 16 and the front section 18. The third and fourth fiber reinforcement layers are particularly helpful in improving the torsional stiffness of the middle section 16 and the front section 18.

[0084] The fifth sheet S5 is located biasedly on the rear end 20 side of the shaft 4. The fifth sheet S5 is approximately trapezoidal in shape. This fifth sheet S5 comprises multiple carbon fibers arranged side by side. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is substantially 0°. In this fifth sheet S5, the width is 72mm, the length of the upper outsole is 145mm, and the length of the lower outsole is 155mm.

[0085] As described above, the carbon fibers contained in the fifth sheet S5 are substantially axially oriented. Therefore, in the fifth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. In this specification, the structure in which the carbon fibers are substantially axially oriented is referred to as a "straight structure." The fifth fiber reinforcement layer has a straight structure. When the shaft 4 flexes, a large tension is applied to these carbon fibers. This tension inhibits further flexural bending of the shaft 4. In other words, these carbon fibers contribute to the bending stiffness of the shaft 4. The fifth fiber reinforcement layer particularly contributes to the bending stiffness of the rear portion 14.

[0086] The sixth sheet S6 is biasedly located on the front end 22 side of the shaft 4. The sixth sheet S6 is approximately trapezoidal in shape. This sixth sheet S6 comprises a plurality of carbon fibers arranged side by side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is 30° or more and 60° or less. In this embodiment, the angle is 45°. In this sixth sheet S6, the width is 18 mm, the length of the upper base is 95 mm, and the length of the lower base is 105 mm.

[0087] The seventh sheet S7 is located biasedly on the front end 22 side of the shaft 4. Axially, the position of the seventh sheet coincides with that of the sixth sheet S6. The seventh sheet S7 is approximately trapezoidal in shape. This seventh sheet S7 comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is -60° or more and -30° or less. In this embodiment, this angle is -45°. The seventh sheet S7 has a width of 18 mm, a length of 95 mm for the upper part, and a length of 105 mm for the lower part.

[0088] The carbon fibers in the seventh sheet S7 are tilted in the opposite direction to those in the sixth sheet S6. Therefore, the carbon fibers in the seventh fiber reinforcement layer are tilted in the opposite direction to those in the sixth fiber reinforcement layer. In this shaft 4, an offset structure is achieved through the sixth and seventh fiber reinforcement layers. The sixth and seventh fiber reinforcement layers contribute to the bending and torsional stiffness of the rear section 14. The sixth and seventh fiber reinforcement layers are particularly helpful in improving the torsional stiffness of the rear section 14.

[0089] The eighth sheet S8 is located biasedly on the rear end 20 side of the shaft 4. The eighth sheet S8 is approximately trapezoidal in shape. This eighth sheet S8 comprises multiple carbon fibers arranged side by side. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is substantially 0°. In this eighth sheet S8, the width is 36 mm, the length of the upper outsole is 235 mm, and the length of the lower outsole is 245 mm.

[0090] As described above, the carbon fibers contained in the eighth sheet S8 are substantially axially oriented. Therefore, in the eighth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. The eighth fiber reinforcement layer has a straight structure. When the shaft 4 flexes, a large tension is applied to these carbon fibers. This tension inhibits further flexural bending of the shaft 4. In other words, these carbon fibers contribute to the bending stiffness of the shaft 4. The eighth fiber reinforcement layer particularly contributes to the bending stiffness of the rear section 14 and the middle section 16.

[0091] The ninth sheet S9 is distributed throughout the entire shaft 4. The ninth sheet S9 is approximately rectangular in shape. It comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is essentially 0°. The ninth sheet S9 has a width of 30 mm and a length of 340 mm.

[0092] As described above, the carbon fibers contained in the ninth sheet S9 are substantially axially oriented. Therefore, in the ninth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. The ninth fiber reinforcement layer has a straight structure. When the shaft 4 flexes, a large tension is applied to these carbon fibers. This tension inhibits further flexural bending of the shaft 4. In other words, these carbon fibers contribute to the bending stiffness of the shaft 4.

[0093] In the shaft 4, a first fiber reinforcement layer, a second fiber reinforcement layer, and a ninth fiber reinforcement layer are distributed between the rear end 20 and the front end 22. These fiber reinforcement layers contribute to the durability of the shaft 4.

[0094] In the manufacturing of the racket shaft 4, Figure 5The sheets shown are wound sequentially onto a mandrel. The first sheet S1 and the second sheet S2 can be wound onto the mandrel in an overlapping manner. The third sheet S3 and the fourth sheet S4 can be wound onto the mandrel in an overlapping manner. The sixth sheet S6 and the seventh sheet S7 can be wound onto the mandrel in an overlapping manner. Other sheets can be wound onto the mandrel together with these sheets. As other sheets, sheets containing glass fibers can be exemplified.

[0095] Wrapping tape is then further wound onto these sheets. These mandrels, prepreg sheets (sheets S1-S9), and wrapping tape are heated in an oven or similar environment. Heating causes the resin in the matrix to flow. Further heating causes the resin to cure, resulting in a molded body. The molded body is then subjected to end-face machining, grinding, and coating to complete the drumstick 4.

[0096] The shaft 4 is made of fiber-reinforced resin. The shaft 4 can also be made of a resin composition that does not contain fibers. The shaft 4 can also be made of metal, wood, etc.

[0097] Figure 6 It means Figure 1 A diagram illustrating a method for determining the frequency of the out-of-plane natural vibration of a racket 2. In this method, the racket 2 is suspended by a string 36. The racket 2 does not have a string 12. In other words, the racket 2 is used without the string 12 in the determination of the frequency of its natural vibration. Figure 6 In this configuration, the axis (Y direction) of the shaft 4 is aligned with the vertical direction. Figure 6 In the middle, the frame 6 is located higher than the shaft 4.

[0098] like Figure 6 As shown, an accelerometer 38 is mounted on the racket 2. The accelerometer 38 is located at the front end of the handle 10. The direction of the accelerometer 38 is the Z direction. The accelerometer 38 has a mass of 3.5g. Next, a vibration is applied to a point Ph on the side of the racket shaft 4 opposite to the accelerometer 38 using an impact hammer (not shown). The input vibration measured by the force pick-up sensor of the impact hammer and the vibration response measured by the accelerometer 38 are transmitted to a vibration frequency analysis device (HP's "Dynamic Signal Analyzer") via an amplifier. Based on the transfer function obtained by this device, the frequency of the out-of-plane natural vibration is calculated. The direction of the out-of-plane natural vibration is mainly the Z direction. In this method, the natural frequency is determined when no part of the racket 2 is firmly fixed. In other words, the natural frequency is determined under free constraint conditions.

[0099] Figure 7 It means through Figure 6 The results of the measurement are shown in the graph. Figure 7 In the diagram, the horizontal axis represents frequency (Hz), and the vertical axis represents the magnitude of acceleration admittance (m / s²). 2 / N). In Figure 7 In the diagram, P1 represents the first-order peak. The frequency at this first-order peak P1 is the out-of-plane first-order natural frequency ωo1. Figure 7 In the diagram, P2 represents the second-order peak. The frequency at this second-order peak P2 is the out-of-plane second-order natural frequency ωo2.

[0100] Figure 8 This is a graph showing the relationship between the out-of-plane first-order natural frequency ωo1 and the out-of-plane second-order natural frequency ωo2 of badminton racket 2. In this graph, the symbol Pr represents... Figure 1-5 Point 2 on the racket shown in the image.

[0101] exist Figure 8 In the equation, the straight line represented by the symbol L1 can be expressed by the following mathematical formula.

[0102] ωo2 = 2.5 × ωo1 + 37.0

[0103] like Figure 8 As shown, point Pr is located higher than line L1. In other words, the coordinates (ωo1, ωo2) of racket 2 have the following mathematical expression (I-1).

[0104] ωo2≥2.5×ωo1+37.0(I-1)

[0105] According to the discoveries made by the inventors, the racket 2 that satisfies the mathematical formula (I-1) is suitable for lob shots. Players using the racket 2 to perform lob shots can easily obtain the desired shuttlecock trajectory. With this racket 2, the trajectory deviation of the shuttlecock in a lob shot is small.

[0106] According to the discoveries of the inventors, when the shuttlecock is struck at the portion of the racket face 32 near the bottom 26 of the frame, the vibration of the out-of-plane second-order mode is primarily excited. According to the discoveries of the inventors, when the shuttlecock is struck at the portion of the racket face 32 near the top 24 of the frame, the vibration of the out-of-plane first-order mode is primarily excited. A typical hitting point in a lob is near the top 24 of the frame. Therefore, in a lob, the vibration of the out-of-plane first-order mode is primarily excited. However, even in a lob, the hitting point can deviate. In the racket 2 that satisfies the above mathematical formula (I-1), the out-of-plane first-order natural frequency ωo1 is relatively small, and the out-of-plane second-order natural frequency ωo2 is relatively large. According to the discoveries of the inventors, in a lob shot using a racket 2 based on a small out-of-plane first-order natural frequency ωo1 and a large out-of-plane second-order natural frequency ωo2, even if the hitting point deviates, the initial velocity deviation of the shuttlecock is small. The reason is that even when the shuttlecock is hit from a position deviating from the intended location, the rebound of racket 2 will not be very small. Because the initial velocity deviation of the shuttlecock is small, the deviation in its trajectory is also small. This racket 2 is suitable for athletes who frequently use lobs. It is also suitable for athletes who emphasize lobs.

[0107] As described above, the typical point of contact for a lob is towards the top of the frame 24. The racket 2 of the present invention is also suitable for shots other than lobs that are hit at the portion of the string face 32 towards the top of the frame 24.

[0108] By changing the position, number, width, and length of the prepreg sheets in the paddle 4, as well as the fiber angle, fiber weight per unit area, and fiber modulus of elasticity, both low frequency ωo1 and high frequency ωo2 can be achieved. A specific example can be provided:

[0109] (a) The fiber reinforcement layer with a straight structure is biased at the rear 14;

[0110] (b) Set the number of fiber reinforcement layers to be increased in the rear 14;

[0111] (c) The fiber reinforcement layer with a large unit area weight is offset at the rear 14;

[0112] (d) The fiber reinforcement layer with high elastic modulus is biased to the rear part 14;

[0113] (e) Set to reduce the number of fiber reinforcement layers in the front 18;

[0114] (f) The fiber reinforcement layer with a small unit area weight is biased to the front 18;

[0115] (g) The fiber reinforcement layer with low elastic modulus is biased to the front part 18, etc.

[0116] In this embodiment, as described above, the high stiffness of the rear portion 14 is achieved through the fifth fiber reinforcement layer obtained from the fifth sheet S5 and the eighth fiber reinforcement layer obtained from the eighth sheet S8. This enables the achievement of a low frequency ωo1 and a high frequency ωo2.

[0117] By adjusting the specifications of components other than the racket shaft 4, both low frequencies ωo1 and high frequencies ωo2 can be achieved. The racket frame 6 is an example of a component capable of influencing frequency. By changing the position, number, width, and length of the prepreg sheets within the racket frame 6, as well as the angle of the fibers, the weight per unit area of ​​the fibers, and the elastic modulus of the fibers, both low frequencies ωo1 and high frequencies ωo2 can be achieved. Specific examples can be provided below.

[0118] (a) The fiber reinforcement layer with a straight structure is biased near the bottom 26 of the frame 6;

[0119] (b) Set the number of fiber reinforcement layers near the bottom 26 of the frame 6;

[0120] (c) The fiber reinforcement layer with a large unit area weight is offset near the bottom 26 of the frame 6;

[0121] (d) The fiber reinforcement layer with high elastic modulus is biased near the bottom 26 of the frame 6;

[0122] (e) Set to reduce the number of fiber reinforcement layers near the top 24 of the frame 6;

[0123] (f) The fiber reinforcement layer with a small unit area weight is offset near the top 24 of the frame 6;

[0124] (g) The fiber reinforcement layer with low elastic modulus is biased near the top 24 of the frame 6, etc.

[0125] exist Figure 8 In the equation, the straight line represented by the symbol L2 can be expressed by the following mathematical formula.

[0126] ωo2 = 2.5 × ωo1 + 44.0

[0127] like Figure 8 As shown, point Pr is located higher than line L2. In other words, the coordinates (ωo1, ωo2) of racket 2 have the following mathematical expression (I-2).

[0128] ωo2≥2.5×ωo1+44.0(I-2)

[0129] According to the discoveries made by the inventors, the racket 2 that satisfies the mathematical formula (I-2) is suitable for lob shots. Players using the racket 2 to perform lob shots can easily obtain the desired shuttlecock trajectory. With the racket 2, the trajectory deviation of the shuttlecock in a lob shot is small.

[0130] exist Figure 8 In the equation, the straight line represented by the symbol L3 can be represented by the following mathematical expression.

[0131] ωo2 = 2.5 × ωo1 + 54.0

[0132] like Figure 8 As shown, point Pr is located higher than line L3. In other words, the coordinates (ωo1, ωo2) of racket 2 have the following mathematical expression (I-3).

[0133] ωo2≥2.5×ωo1+54.0(I-3)

[0134] According to the discoveries made by the inventors, the racket 2 that satisfies the mathematical formula (I-3) is suitable for lob shots. Players using this racket 2 to perform lob shots can easily obtain the desired shuttlecock trajectory. With this racket 2, the trajectory deviation of the shuttlecock in a lob shot is small.

[0135] exist Figure 8 In the equation, the straight line represented by the symbol L4 can be expressed by the following mathematical formula.

[0136] ωo2=179

[0137] like Figure 8 As shown, point Pr is located higher than line L4. The frequency ωo2 of point Pr is above 179. In other words, the coordinates (ωo1, ωo2) of racket 2 have the following mathematical expression (I-4).

[0138] ωo2≥179(I-4)

[0139] According to the discoveries made by the inventors, racket 2 that satisfies the mathematical formula (I-4) is suitable for lob shots. In lob shots using racket 2, the shuttlecock flies at high speed.

[0140] exist Figure 8 In the equation, the straight line represented by the symbol L5 can be represented by the following mathematical expression.

[0141] ωo2=184

[0142] like Figure 8 As shown, point Pr is located higher than line L5. The frequency ωo2 of point Pr is above 184. In other words, the coordinates (ωo1, ωo2) of racket 2 have the following mathematical expression (I-5).

[0143] ωo2≥184(I-5)

[0144] According to the discoveries made by the inventors, racket 2 that satisfies the mathematical formula (I-5) is suitable for lob shots. In lob shots using racket 2, the shuttlecock flies at high speed.

[0145] Figure 9 This is a developed view illustrating a prepreg sheet structure for the shaft of a badminton racket according to another embodiment. This prepreg sheet structure has 11 prepreg sheets (i.e., sheets). Specifically, the prepreg sheet structure has a first sheet S1, a second sheet S2, a third sheet S3, a fourth sheet S4, a fifth sheet S5, a sixth sheet S6, a seventh sheet S7, an eighth sheet S8, a ninth sheet S9, a tenth sheet S10, and an eleventh sheet S11. Multiple fiber reinforcement layers are formed from these prepreg sheets using a method described later. Specifically, the first fiber reinforcement layer is formed by the first sheet S1, the second fiber reinforcement layer is formed by the second sheet S2, the third fiber reinforcement layer is formed by the third sheet S3, the fourth fiber reinforcement layer is formed by the fourth sheet S4, the fifth fiber reinforcement layer is formed by the fifth sheet S5, the sixth fiber reinforcement layer is formed by the sixth sheet S6, the seventh fiber reinforcement layer is formed by the seventh sheet S7, the eighth fiber reinforcement layer is formed by the eighth sheet S8, the ninth fiber reinforcement layer is formed by the ninth sheet S9, the tenth fiber reinforcement layer is formed by the tenth sheet S10, and the eleventh fiber reinforcement layer is formed by the eleventh sheet S11.

[0146] Figure 9 The left and right directions in the middle are the axis of the racket shaft. Figure 9 In the diagram, the positions of backend 20 and frontend 22 are indicated by arrows. For ease of explanation, in... Figure 9 In the middle, the scale in the left-right direction (axial direction) is inconsistent with the scale in the up-down direction.

[0147] A first sheet S1 is distributed throughout the entire shaft. The first sheet S1 is generally rectangular in shape. The first sheet S1 comprises a plurality of carbon fibers arranged side by side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is 30° or more and 60° or less. In this embodiment, the angle is 45°. The first sheet S1 has a width of 82 mm and a length of 340 mm.

[0148] The second sheet S2 is distributed throughout the entire shaft. The second sheet S2 is approximately rectangular in shape. It comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is -60° or higher and -30° or lower. In this embodiment, this angle is -45°. The second sheet S2 has a width of 82 mm and a length of 340 mm.

[0149] The carbon fibers in the second sheet S2 are tilted in the opposite direction to those in the first sheet S1. Therefore, the carbon fibers in the second fiber reinforcement layer are tilted in the opposite direction to those in the first fiber reinforcement layer. In this racket shaft, an offset structure is achieved through the first and second fiber reinforcement layers. The first and second fiber reinforcement layers contribute to the bending and torsional stiffness of the racket shaft. The first and second fiber reinforcement layers are particularly beneficial to the torsional stiffness of the racket shaft.

[0150] A third sheet S3 is located approximately at the center of the shaft. The third sheet S3 is roughly parallelogram-shaped. This third sheet S3 comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is 30° or more and 60° or less. In this embodiment, this angle is 45°. The third sheet S3 has a width of 38 mm and a length of 70 mm.

[0151] A fourth sheet S4 is located approximately at the center of the shaft. Axially, the fourth sheet S4 is positioned identically to the third sheet S3. The fourth sheet S4 is approximately parallelogram-shaped. It comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is between -60° and -30°. In this embodiment, this angle is -45°. The fourth sheet S4 has a width of 38 mm and a length of 70 mm.

[0152] The carbon fibers in the fourth sheet S4 are tilted in the opposite direction to those in the third sheet S3. Therefore, the carbon fibers in the fourth fiber reinforcement layer are tilted in the opposite direction to those in the third fiber reinforcement layer. In this racket shaft, an offset structure is achieved through the third and fourth fiber reinforcement layers. The third and fourth fiber reinforcement layers contribute to the bending and torsional stiffness in the middle section. The third and fourth fiber reinforcement layers are particularly helpful for the torsional stiffness in the middle section.

[0153] The fifth sheet S5 is offset to the front 22 side of the shaft. The fifth sheet S5 is approximately trapezoidal in shape. It comprises multiple parallel carbon fibers. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is essentially 0°. The fifth sheet S5 has a width of 76 mm, a top length of 105 mm, and a bottom length of 115 mm.

[0154] As described above, the carbon fibers contained in the fifth sheet S5 are substantially axially oriented. Therefore, in the fifth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. In this specification, the structure in which the carbon fibers are substantially axially oriented is referred to as a "straight structure." The fifth fiber reinforcement layer has a straight structure. During shaft flexure, a large tension is applied to these carbon fibers. This tension inhibits further shaft flexure. In other words, these carbon fibers contribute to the bending stiffness of the shaft. The fifth fiber reinforcement layer is particularly helpful for the bending stiffness of the front section.

[0155] The sixth sheet S6 is located biasedly on the rear end 20 side of the shaft. The sixth sheet S6 is approximately trapezoidal in shape. It comprises multiple parallel carbon fibers. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is essentially 0°. The sixth sheet S6 has a width of 76 mm, a length of 155 mm for the upper part, and a length of 165 mm for the lower part.

[0156] As described above, the carbon fibers contained in the sixth sheet S6 are substantially axially oriented. Therefore, in the sixth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. The sixth fiber reinforcement layer has a straight structure. During shaft flexure, a large tension is applied to these carbon fibers. This tension inhibits further shaft flexure. In other words, these carbon fibers contribute to the bending stiffness of the shaft. The sixth fiber reinforcement layer is particularly helpful for the bending stiffness at the rear.

[0157] A seventh sheet S7 is located approximately at the center of the shaft. The seventh sheet S7 is roughly parallelogram-shaped. This seventh sheet S7 comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is 30° or more and 60° or less. In this embodiment, this angle is 45°. The seventh sheet S7 has a width of 38 mm and a length of 110 mm.

[0158] The eighth sheet S8 is located approximately at the center of the shaft. Axially, the position of the eighth sheet S8 coincides with that of the seventh sheet S7. The shape of the eighth sheet S8 is approximately a parallelogram. This eighth sheet S8 comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is inclined relative to the axial direction. The angle between the extension direction of the carbon fiber and the axial direction is -60° to -30°. In this embodiment, this angle is -45°. The eighth sheet S8 has a width of 38 mm and a length of 110 mm.

[0159] The ninth sheet S9 is located biasedly on the front end 22 side of the shaft. The ninth sheet S9 is approximately trapezoidal in shape. This ninth sheet S9 comprises multiple carbon fibers arranged side by side. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is substantially 0°. In this ninth sheet S9, the width is 76 mm, the length of the upper part is 85 mm, and the length of the lower part is 95 mm.

[0160] As described above, the carbon fibers contained in the ninth sheet S9 are substantially axially oriented. Therefore, in the ninth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. The ninth fiber reinforcement layer has a straight structure. During shaft flexure, a large tension is applied to these carbon fibers. This tension inhibits further shaft flexure. In other words, these carbon fibers contribute to the bending stiffness of the shaft. The ninth fiber reinforcement layer is particularly helpful for the bending stiffness of the front section.

[0161] The tenth sheet S10 is located biasedly on the rear end 20 side of the shaft. The tenth sheet S10 is approximately trapezoidal in shape. It comprises multiple parallel carbon fibers. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is substantially 0°. The tenth sheet S10 has a width of 76 mm, a length of 135 mm for the upper outsole, and a length of 145 mm for the lower outsole.

[0162] As described above, the carbon fibers contained in the tenth sheet S10 are substantially axially oriented. Therefore, in the tenth fiber reinforcement layer, the carbon fibers are also substantially axially oriented. The tenth fiber reinforcement layer has a straight structure. During shaft flexure, a large tension is applied to these carbon fibers. This tension inhibits further shaft flexure. In other words, these carbon fibers contribute to the bending stiffness of the shaft. The tenth fiber reinforcement layer is particularly helpful for the bending stiffness at the rear.

[0163] The eleventh piece of material S11 is distributed throughout the entire shaft. The eleventh piece of material S11 is approximately rectangular in shape. It comprises multiple carbon fibers arranged side-by-side. The extension direction of each carbon fiber is aligned with the axial direction. In other words, the angle between the extension direction of the carbon fiber and the axial direction is essentially 0°. The eleventh piece of material S11 has a width of 4 mm and a length of 340 mm.

[0164] As described above, the carbon fibers contained in the eleventh sheet S11 are substantially axially oriented. Therefore, in the eleventh fiber reinforcement layer, the carbon fibers are also substantially axially oriented. The eleventh fiber reinforcement layer has a straight structure. When the racket shaft bends, a large tension is applied to these carbon fibers. This tension inhibits further deflection of the racket shaft. In other words, these carbon fibers contribute to the bending stiffness of the racket shaft.

[0165] In this racket shaft, a first fiber reinforcement layer, a second fiber reinforcement layer, and an eleventh fiber reinforcement layer are distributed between the rear end 20 and the front end 22. These fiber reinforcement layers contribute to the durability of the racket shaft.

[0166] In the manufacturing of this racket shaft, Figure 9 The sheets shown are wound sequentially onto a mandrel. The first sheet S1 and the second sheet S2 can be wound onto the mandrel in an overlapping manner. The third sheet S3 and the fourth sheet S4 can be wound onto the mandrel in an overlapping manner. The sixth sheet S6 and the seventh sheet S7 can be wound onto the mandrel in an overlapping manner. Other sheets can be wound onto the mandrel together with these sheets. As other sheets, sheets containing glass fibers can be exemplified.

[0167] On these sheets, a winding tape is further wound. These mandrels, prepreg sheets (sheets S1-S11), and winding tape are heated in an oven or similar environment. Heating causes the resin in the matrix to flow. Further heating causes the resin to cure, resulting in a molded body. This molded body is then subjected to end-face machining, grinding, and coating to complete the hammer handle.

[0168] The racket shaft is made of fiber-reinforced resin. The shaft can also be made of a resin composition that does not contain fibers. The shaft can also be made of metal, wood, etc.

[0169] Figure 10 This is an explanatory diagram illustrating a method for measuring the frequency of the in-plane natural vibration of a racket 102 according to another embodiment. In this method, the racket 102 is suspended by a string 36. The racket 102 does not have strings. In other words, the racket 102 without strings is used in the measurement of the frequency of its natural vibration. Figure 10 In this configuration, the axial direction (Y direction) of the shaft 104 is aligned with the vertical direction. Figure 10 In the middle, the shaft 104 is located lower than the frame 106.

[0170] like Figure 10As shown, an accelerometer 38 is mounted on the racket 102. The accelerometer 38 is located at the front end of the handle 110. The direction of the accelerometer 38 is the X-direction. The accelerometer 38 has a mass of 3.5g. Next, a point Ph on the side of the handle 110 opposite to the accelerometer 38 is vibrated using an impact hammer (not shown). The input vibration measured by the force sensor of the impact hammer and the vibration response measured by the accelerometer 38 are transmitted to a frequency analysis device (HP's "Dynamic Signal Analyzer") via an amplifier. Based on the transfer function obtained by this device, the frequency of the in-plane natural vibration is calculated. The direction of the in-plane natural vibration is primarily the X-direction. In this method, the natural frequency is determined with no part of the racket 102 being firmly fixed. In other words, the natural frequency is determined under free constraint conditions.

[0171] Figure 11 It means through Figure 10 The results of the measurement are shown in the graph. Figure 11 In the diagram, the horizontal axis represents frequency (Hz), and the vertical axis represents the magnitude of acceleration admittance (m / s²). 2 / N). In Figure 11 In the diagram, P1 represents a first-order peak. The frequency of this first-order peak P1 is the in-plane first-order natural frequency ωi1. Figure 11 In the diagram, P2 represents the second-order peak. The frequency of this second-order peak P2 is the in-plane second-order natural frequency ωi2.

[0172] Figure 12 It means through Figure 10 The graph shows the relationship between the measured in-plane first-order natural frequency ωi1 and the in-plane second-order natural frequency ωi2. In this graph, the symbol Pr represents... Figure 15 The point on the racket shown.

[0173] exist Figure 12 In the equation, the straight line represented by the symbol L1 can be expressed by the following mathematical formula.

[0174] ωi2 = 3.6 × ωi1 + 5.0

[0175] like Figure 12 As shown, point Pr is located on the upper side compared to line L1. In other words, the coordinates (ωi1, ωi2) of the racket 102 have the following mathematical expression (II-1).

[0176] ωi2≥3.6×ωi1+5.0(II-1)

[0177] According to the discoveries made by the inventors, a racket 102 that satisfies the mathematical formula (II-1) is suitable for lobbed shots. A player using this racket 102 to lobbed shots can easily obtain a predetermined shuttlecock trajectory. With this racket 102, the trajectory deviation of the shuttlecock in a lobbed shot is small.

[0178] According to the discoveries of the inventors, when a shuttlecock is struck at the portion of the racket face near the bottom of the frame, the vibration of the second-order in-plane mode is primarily excited. According to the discoveries of the inventors, when a shuttlecock is struck at the portion of the racket face near the top of the frame, the vibration of the first-order in-plane mode is primarily excited. A typical hitting point in a slice shot is near the top of the frame. Therefore, in a slice shot, the vibration of the first-order in-plane mode is primarily excited. However, even in a slice shot, the hitting point can deviate. In the racket 102 that satisfies the above mathematical formula (II-1), the in-plane first-order natural frequency ωi1 is relatively small, and the in-plane second-order natural frequency ωi2 is relatively large. According to the discoveries of the inventors, in a slice shot using a racket 102 based on a racket with a small in-plane first-order natural frequency ωi1 and a large in-plane second-order natural frequency ωi2, even if the hitting point deviates, the initial velocity deviation of the shuttlecock is small. The reason is that even if the shuttlecock is struck from a position deviating from the predetermined position, the rebound of the racket 102 will not be very small. Because the initial velocity deviation of the shuttlecock is small, the trajectory deviation of the shuttlecock is also small. This racket 102 is suitable for athletes who frequently use high slice shots. This racket 102 is also suitable for athletes who emphasize high slice shots.

[0179] As mentioned above, the typical contact point in a chip shot is towards the top of the frame. The racket 102 is also suitable for shots other than chip shots that are hit at a location near the top of the frame on the string face.

[0180] By changing the position, number, width, and length of the prepreg sheets in the racket arm 104, as well as the fiber angle, fiber weight per unit area, and fiber modulus of elasticity, both low frequency ωi1 and high frequency ωi2 can be achieved. A specific example can be given:

[0181] (a) The fiber reinforcement layer with a straight structure is biased to the rear;

[0182] (b) Set the number of fiber reinforcement layers at the rear;

[0183] (c) The fiber reinforcement layer with a large unit area weight is offset at the rear;

[0184] (d) The fiber reinforcement layer with high elastic modulus is biased to the rear part;

[0185] (e) Set to reduce the number of fiber reinforcement layers at the front;

[0186] (f) Position the fiber reinforcement layer with a small unit area weight at the front;

[0187] (g) Positioning the fiber reinforcement layer with fibers having a low elastic modulus towards the front, etc. In Figure 9 In the embodiment shown, as described above, high stiffness at the rear is achieved through the fifth fiber reinforcement layer obtained from the fifth sheet S5 and the eighth fiber reinforcement layer obtained from the eighth sheet S8. This results in a low frequency ωi1 and a high frequency ωi2.

[0188] Both low frequencies ωi1 and high frequencies ωi2 can be achieved by adjusting the specifications of components other than the racket shaft 104. The racket frame 106 is an example of a component capable of influencing frequency. By changing the position, number, width, and length of the prepreg sheets, the angle of the fibers, the weight per unit area of ​​the fibers, and the elastic modulus of the fibers, both low and high frequencies ωi1 and ωi2 can be achieved. Specific examples include:

[0189] (a) The fiber reinforcement layer with a straight structure is offset near the bottom of the frame 106;

[0190] (b) Set the number of fiber reinforcement layers near the bottom of the frame 106;

[0191] (c) The fiber reinforcement layer with a large unit area weight is offset near the bottom of the frame 106;

[0192] (d) The fiber reinforcement layer with high elastic modulus is biased near the bottom of the frame 106;

[0193] (e) Set to reduce the number of fiber reinforcement layers near the top of the frame 106;

[0194] (f) The fiber reinforcement layer with a small unit area weight is offset near the top of the frame of the racket frame 106;

[0195] (g) The fiber reinforcement layer with low elastic modulus is biased near the top of the frame of the racket frame 106, etc.

[0196] exist Figure 12 In the equation, the straight line represented by the symbol L2 can be expressed by the following mathematical formula.

[0197] ωi2 = 3.6 × ωi1 + 16.0

[0198] like Figure 12 As shown, point Pr is located on the upper side compared to line L2. In other words, the coordinates (ωi1, ωi2) of the racket 102 have the following mathematical expression (II-2).

[0199] ωi2≥3.6×ωi1+16.0(II-2)

[0200] According to the discoveries made by the inventors, the racket 102 that satisfies the mathematical formula (II-2) is suitable for lobbed shots. Athletes using the racket 102 to lobbed shots can easily obtain a predetermined shuttlecock trajectory. With the racket 102, the trajectory deviation of the shuttlecock in a lobbed shot is small.

[0201] exist Figure 12 In the equation, the straight line represented by the symbol L3 can be represented by the following mathematical expression.

[0202] ωi2≥3.6×ωi1+29.0

[0203] like Figure 12 As shown, point Pr is located higher than line L3. In other words, the coordinates (ωi1, ωi2) of racket 102 have the following mathematical expression (II-3).

[0204] ωi2≥3.6×ωi1+29.0(II-3)

[0205] According to the discoveries made by the inventors, the racket 102 that satisfies the mathematical formula (II-3) is suitable for lobbed shots. Athletes using the racket 102 to lobbed shots can easily obtain a predetermined shuttlecock trajectory. With this racket 102, the trajectory deviation of the shuttlecock in a lobbed shot is small.

[0206] exist Figure 12 In the equation, the straight line represented by the symbol L4 can be expressed by the following mathematical formula.

[0207] ωi2=203

[0208] like Figure 12 As shown, point Pr is located higher than line L4. The frequency ωi2 of point Pr is 203 or higher. In other words, the coordinates (ωi1, ωi2) of the racket 102 have the following mathematical expression (II-4).

[0209] ωi2≥203(II-4)

[0210] According to the discoveries made by the inventors, the racket 102 that satisfies the mathematical formula (II-4) is suitable for lobbed shots. In lobbed shots using the racket 102, the shuttlecock flies at high speed.

[0211] exist Figure 12 In the equation, the straight line represented by the symbol L5 can be represented by the following mathematical expression.

[0212] ωi2=208

[0213] like Figure 12As shown, point Pr is located higher than line L5. The frequency ωi2 of point Pr is 208 or higher. In other words, the coordinates (ωi1, ωi2) of the racket 102 have the following mathematical expression (II-5).

[0214] ωi2≥208(II-5)

[0215] According to the discoveries made by the inventors, a racket 102 that satisfies the mathematical formula (II-5) is suitable for lobbed shots. In a lobbed shot using this racket 102, the shuttlecock flies at high speed.

[0216] Example

[0217] While the effects of the badminton racket in the embodiments are explained below, the scope of the disclosure in this specification should not be interpreted in a limiting way based on the description of these embodiments.

[0218] [Experiment I]

[0219] [Example I-1]

[0220] Making with Figure 5 The racket shaft is shown to have a prepreg sheet structure. Each prepreg sheet contains carbon fiber. The tensile modulus (tensile elastic modulus) of this carbon fiber is 35 tf / mm. 2 A badminton racket is made by mounting a frame, neck, forehand, and handle of standard stiffness and quality, typically found in commercially available badminton rackets, onto the shaft. The racket has a first out-of-plane natural frequency ωo1 of 54 Hz and a second out-of-plane natural frequency ωo2 of 189 Hz. The racket's coordinates are... Figure 8 The symbol Pr represents the value in the middle.

[0221] [Examples I-2 to I-11 and Comparative Examples I-1 to I-8]

[0222] Except for setting the prepreg sheet structure as shown in Tables 1 to 4, the rest of the setup was the same as in Example I-1, resulting in badminton rackets of Examples I-2 to I-11 and Comparative Examples I-1 to I-8. The shaft widths of these rackets using the prepreg sheet are shown in Tables 1 to 4 below. The out-of-plane first natural frequency ωo1 and out-of-plane second natural frequency ωo2 of these rackets are shown in Tables 1 to 4 below. Figure 8 middle.

[0223] [stability]

[0224] A badminton shuttlecock is launched using a shuttlecock launcher. An athlete performs a lob shot on the shuttlecock, and the trajectory is photographed. The image is analyzed to determine the height of the shuttlecock as it passes over the net. Twenty measurements are performed, and the standard deviation of the height is calculated. Based on this standard deviation, the rackets are graded. The grading criteria are as described below. The results are shown in Tables 1 through 4 below.

[0225] A: Standard deviation is less than 0.14m

[0226] B: Standard deviation is greater than 0.14m and less than 0.20m

[0227] C: Standard deviation is above 0.20m

[0228] [Resilience]

[0229] To evaluate the stability described above, the speed of the shuttlecock passing over the net was measured. Twenty measurements were performed, and the average speed was calculated. Based on this average speed, the racket was rated. The rating criteria are as follows. The results are shown in Tables 1 to 4 below.

[0230] A: The average speed is above 19.0 m / s.

[0231] B: Average speed is above 18.0 m / s and below 19.0 m / s

[0232] C: Average speed less than 18.0 m / s

[0233] [Table 1]

[0234] Table 1 Evaluation Results

[0235]

[0236] [Table 2]

[0237] Table 2 Evaluation Results

[0238]

[0239] [Table 3]

[0240] Table 3 Evaluation Results

[0241]

[0242] [Table 4]

[0243] Table 4 Evaluation Results

[0244]

[0245] As shown in Tables 1 to 4, the shuttlecock trajectory is stable in all badminton rackets used in the various embodiments when performing lobs or slices. This evaluation result demonstrates the obvious superiority of this racket.

[0246] [Experiment II]

[0247] [Example II-1]

[0248] Making with Figure 9The racket shaft is shown as a prepreg sheet structure. Each prepreg sheet contains carbon fiber. The tensile modulus of this carbon fiber is 24 tf / mm². 2 A badminton racket is made by mounting a frame, neck, forehand, and handle of standard stiffness and quality, as used in commercially available badminton rackets, onto the shaft. The racket has a first-order in-plane natural frequency ωi1 of 52 Hz and a second-order in-plane natural frequency ωi2 of 217 Hz.

[0249] [Examples II-2 to II-10 and Comparative Examples II-1 to II-8]

[0250] Except for setting the prepreg sheet structure as shown in Tables 5 to 8, the rest of the setup was the same as in Example II-1, resulting in badminton rackets of Examples II-2 to II-10 and Comparative Examples II-1 to II-8. The shaft widths of these rackets using the prepreg sheet are shown in Tables 5 to 8 below. The in-plane first natural frequency ωi1 and in-plane second natural frequency ωi2 of these rackets are shown in Tables 5 to 8 below. Figure 12 middle.

[0251] [stability]

[0252] A badminton shuttlecock is launched using a shuttlecock launcher. A player attempts to slice the shuttlecock high, and the trajectory is photographed. The images are analyzed to determine the height of the shuttlecock as it passes the net. Twenty measurements are performed, and the standard deviation of the height is calculated. Based on this standard deviation, the rackets are graded. The grading criteria are as described below. The results are shown in Tables 5 through 8.

[0253] A: Standard deviation is less than 0.14m

[0254] B: Standard deviation is greater than 0.14m and less than 0.20m

[0255] C: Standard deviation is above 0.20m

[0256] [Resilience]

[0257] To evaluate the stability described above, the speed of the shuttlecock passing over the net was measured. Twenty measurements were performed, and the average speed was calculated. Based on this average speed, the racket was rated. The rating criteria are as follows. The results are shown in Tables 5 to 8 below.

[0258] A: The average speed is above 19.0 m / s.

[0259] B: Average speed is above 18.0 m / s and below 19.0 m / s

[0260] C: Average speed less than 18.0 m / s

[0261] [Table 5]

[0262] Table 5 Evaluation Results

[0263]

[0264] [Table 6]

[0265] Table 6 Evaluation Results

[0266]

[0267] [Table 7]

[0268] Table 7 Evaluation Results

[0269]

[0270] [Table 8]

[0271] Table 8 Evaluation Results

[0272]

[0273] As shown in Tables 5 to 8, the trajectory of the shuttlecock in the high-spinning shot is stable in all the badminton rackets described in the various embodiments. This evaluation result demonstrates the obvious superiority of this racket.

[0274] [Project 1]

[0275] A badminton racket that has:

[0276] A racket handle with a rear end and a front end.

[0277] A handle for insertion near the rear end of the racket shaft, and

[0278] A racket frame is mounted on the racket shaft near the front end;

[0279] The out-of-plane first natural frequency ωo1 (Hz) and out-of-plane second natural frequency ωo2 (Hz) of the badminton racket in its natural vibration under free constraint conditions satisfy the following mathematical formula (I-1).

[0280] ωo2≥2.5×ωo1+37.0(I-1)

[0281] [Project 2]

[0282] According to Project 1, the badminton racket satisfies the following mathematical formula (I-2).

[0283] ωo2≥2.5×ωo1+44.0(I-2)

[0284] [Project 3]

[0285] According to Project 2, the badminton racket satisfies the following mathematical formula (I-3).

[0286] ωo2≥2.5×ωo1+54.0(I-3)

[0287] [Project 4]

[0288] The badminton racket according to any one of items 1 to 3, wherein the frequency ωo2 is 179 Hz or higher.

[0289] [Project 5]

[0290] According to the badminton racket described in Project 4, the frequency ωo2 is above 184Hz.

[0291] [Project 6]

[0292] A badminton racket that has:

[0293] A racket handle with a rear end and a front end.

[0294] A handle for insertion near the rear end of the racket shaft, and

[0295] A racket frame is mounted on the racket shaft near the front end;

[0296] The in-plane first natural frequency ωi1 (Hz) and in-plane second natural frequency ωi2 (Hz) of the badminton racket under free constraint conditions satisfy the following mathematical formula (II-1).

[0297] ωi2≥3.6×ωi1+5.0(II-1)

[0298] [Project 7]

[0299] According to Project 6, the badminton racket satisfies the following mathematical formula (II-2).

[0300] ωi2≥3.6×ωi1+16.0(II-2)

[0301] [Project 8]

[0302] According to Project 7, the badminton racket satisfies the following mathematical formula (II-3).

[0303] ωi2≥3.6×ωi1+29.0(II-3)

[0304] [Project 9]

[0305] The badminton racket according to any one of items 6 to 8, wherein the frequency ωi2 is 203Hz or higher.

[0306] [Project 10]

[0307] According to the badminton racket described in Project 9, the frequency ωi2 is above 208Hz.

[0308] [Industry availability]

[0309] The badminton racket described above is suitable for players who frequently use a lob or slice shot. It is also suitable for players with other hitting styles who frequently use a shot with the contact point closer to the top of the frame.

Claims

1. A shuttlecock racquet characterized in that, Possessing: a racket shaft having a rear end and a front end, a handle for insertion near the rear end of the racket shaft, and a racket frame mounted on the racket shaft near the front end; the racket satisfies the following mathematical expression (I-1) in the face-out first order natural frequency ωo1 and the face-out second order natural frequency ωo2 in the natural vibration of the racket under free constraint conditions measured at the front end of the handle: ωo2 ≥ 2.5 x ωo1 + 37.0 (I-1) The units of the natural frequencies ωo1 and ωo2 are Hz.

2. The shuttlecock according to claim 1, wherein, The racket satisfies the following mathematical expression (I-2): ωo2 ≥ 2.5 x ωo1 + 44.0 (I-2).

3. The shuttlecock according to claim 2, wherein, The racket satisfies the following mathematical expression (I-3): ωo2 ≥ 2.5 x ωo1 + 54.0 (I-3).

4. The shuttlecock according to any one of claims 1 to 3, wherein, The frequency ωo2 is 179 Hz or more.

5. The shuttlecock according to claim 4, wherein, The frequency ωo2 is 184 Hz or more.

6. A shuttlecock racquet characterized in that, Possessing: a racket shaft having a rear end and a front end, a handle for insertion near the rear end of the racket shaft, and a racket frame mounted on the racket shaft near the front end; the racket satisfies the following mathematical expression (II-1) in the face-in first order natural frequency ωi1 and the face-in second order natural frequency ωi2 in the natural vibration of the racket under free constraint conditions measured at the front end of the handle: ωi2 ≥ 3.6 x ωi1 + 5.0 (II-1) The units of the natural frequencies ωi1 and ωi2 are Hz.

7. The shuttlecock according to claim 6, wherein, The racket satisfies the following mathematical expression (II-2): ωi2 ≥ 3.6 x ωi1 + 16.0 (II-2).

8. The shuttlecock according to claim 7, wherein, The racket satisfies the following mathematical expression (II-3): ωi2 ≥ 3.6 x ωi1 + 29.0 (II-3).

9. The shuttlecock according to any one of claims 6 to 8, wherein, The frequency ωi2 is 203 Hz or more.

10. The shuttlecock according to claim 9, wherein, The frequency ωi2 is 208 Hz or more.

Images